"""### 谜题描述
[Description]
# BBEH Word Sorting

This task is composed of two subtasks.

Subtask 1: This subtask is from the
[BIG-Bench Mistake](https://arxiv.org/pdf/2311.08516). This task involves
finding the first mistake in an existing chain-of-thought sequence, used to
answer a Word Sorting question in the original BBH dataset. In each example,
the target answer is either the number where the first mistake occurred, or
that there are no mistakes in the CoT sequence. These CoT sequences are
generated by prompting PaLM 2 Unicorn on the original BBH dataset at
temperature = 0. The newline is used as a stop token so that each
intermediate step can be prepended with *Thought 1:* , *Thought 2: *, etc.
Further information on the prompting and generation process can be found in
the original work.

Subtask 2: The second sub-task is sorting a list of words given a new
alphabet order (examples include: an alphabet order that is the same as
English but two letters are swapped in the order, an alphabet order that is
the same as English but one/two letters are moved to the beginning/end of the
order, or a completely new order). This task requires going against a strong
prior and sorting words in a non-typical way.

[/Description]
<example_1>

You are an expert in word sorting. You will be provided with a list of words and the steps taken, in the form of thoughts, to arrange them in alphabetical order.
Your job is to identify the first step that was a mistake in reasoning about the order of the words. This can be misunderstanding the order of
the alphabet or getting the word or letter wrong or missing a word entirely.
Q: Sort the following words alphabetically: List: apocalypse tote apostle gay kauffman dicta hog prowl aunt calm carboxy dishevel orifice tearful karate ellen
Thought 1: I should start by looking at the first letter of the words in the list. The first letter: \"apocalypse\": \"a\" (1). \"tote\": \"t\" (20). \"apostle\": \"a\" (1). \"gay\": \"g\" (7). \"kauffman\": \"k\" (11). \"dicta\": \"d\" (4). \"hog\": \"h\" (8). \"prowl\": \"p\" (16). \"aunt\": \"a\" (1). \"calm\": \"c\" (3). \"carboxy\": \"c\" (3). \"dishevel\": \"d\" (4). \"orifice\": \"o\" (15). \"tearful\": \"t\" (20). \"karate\": \"k\" (11). \"ellen\": \"e\" (5).
Thought 2: We now have: (1) [\"apocalypse\" ? \"apostle\" ? \"aunt\" ? \"calm\" ? \"carboxy\"] < (3) \"dicta\" < (4) [\"dishevel\" ? \"dicta\"] < (5) \"ellen\" < (7) \"gay\" < (8) \"hog\" < (11) [\"kauffman\" ? \"karate\"] < (15) \"orifice\" < (16) \"prowl\" < (20) [\"tearful\" ? \"tote\"].
Thought 3: Now let's sort this subpart [\"apocalypse\" ? \"apostle\" ? \"aunt\" ? \"calm\" ? \"carboxy\"] by looking at their second letters. The second letter: \"apocalypse\": \"p\" (16). \"apostle\": \"p\" (16). \"aunt\": \"u\" (21). \"calm\": \"a\" (1). \"carboxy\": \"a\" (1).
Thought 4: We now have: (1) \"calm\" < (16) [\"apocalypse\" ? \"apostle\"] < (21) \"aunt\" < (26) \"carboxy\" for the subpart. Hence, we have \"calm\" < [\"apocalypse\" ? \"apostle\"] < \"aunt\" < \"carboxy\" < \"dicta\" < [\"dishevel\" ? \"dicta\"] < \"ellen\" < \"gay\" < \"hog\" < [\"kauffman\" ? \"karate\"] < \"orifice\" < \"prowl\" < [\"tearful\" ? \"tote\"].
Thought 5: Now let's sort this subpart [\"apocalypse\" ? \"apostle\"] by looking at their third letters. The third letter: \"apocalypse\": \"o\" (15). \"apostle\": \"s\" (19).
Thought 6: We now have: (15) \"apocalypse\" < (19) \"apostle\" for the subpart. Hence, we have \"calm\" < \"apocalypse\" < \"apostle\" < \"aunt\" < \"carboxy\" < \"dicta\" < [\"dishevel\" ? \"dicta\"] < \"ellen\" < \"gay\" < \"hog\" < [\"kauffman\" ? \"karate\"] < \"orifice\" < \"prowl\" < [\"tearful\" ? \"tote\"].
Thought 7: Now let's sort this subpart [\"dishevel\" ? \"dicta\"] by looking at their second letters. The second letter: \"dishevel\": \"i\" (9). \"dicta\": \"i\" (9).
Thought 8: We now have: (9) [\"dishevel\" ? \"dicta\"] for the subpart. Hence, we have \"calm\" < \"apocalypse\" < \"apostle\" < \"aunt\" < \"carboxy\" < \"dicta\" < [\"dishevel\" ? \"dicta\"] < \"ellen\" < \"gay\" < \"hog\" < [\"kauffman\" ? \"karate\"] < \"orifice\" < \"prowl\" < [\"tearful\" ? \"tote\"].
Thought 9: Now let's sort this subpart [\"kauffman\" ? \"karate\"] by looking at their second letters. The second letter: \"kauffman\": \"a\" (1). \"karate\": \"a\" (1).
Thought 10: We now have: (1) [\"kauffman\" ? \"karate\"] for the subpart. Hence, we have \"calm\" < \"apocalypse\" < \"apostle\" < \"aunt\" < \"carboxy\" < \"dicta\" < [\"dishevel\" ? \"dicta\"] < \"ellen\" < \"gay\" < \"hog\" < [\"kauffman\" ? \"karate\"] < \"orifice\" < \"prowl\" < [\"tearful\" ? \"tote\"].
Thought 11: Now let's sort this subpart [\"tearful\" ? \"tote\"] by looking at their second letters. The second letter: \"tearful\": \"e\" (5). \"tote\": \"o\" (15).
Thought 12: We now have: (5) \"tearful\" < (15) \"tote\" for the subpart. Hence, we have \"calm\" < \"apocalypse\" < \"apostle\" < \"aunt\" < \"carboxy\" < \"dicta\" < [\"dishevel\" ? \"dicta\"] < \"ellen\" < \"gay\" < \"hog\" < [\"kauffman\" ? \"karate\"] < \"orifice\" < \"prowl\" < \"tearful\" < \"tote\".
Thought 13: I have now sorted all the words. The answer is apocalypse apostle aunt carboxy calm dicta dishevel ellen gay hog kauffman karate orifice prowl tearful tote
Q: Is there a mistake in this sequence? Write \"No\" if there are no mistakes, or the number N if there is a mistake in Thought N.

</example_1>
<example_2>

You are an expert in word sorting. You will be provided with a list of words and the steps taken, in the form of thoughts, to arrange them in alphabetical order.
Your job is to identify the first step that was a mistake in reasoning about the order of the words. This can be misunderstanding the order of
the alphabet or getting the word or letter wrong or missing a word entirely.
Q: Sort the following words alphabetically: List: shutdown beebread conveyor courtyard semantic aqueduct lacewing grown mummy infinitude tennessee taillight monarch neural aristocrat topheavy flagler deviate
Thought 1: I should start by looking at the first letter of the words in the list. The first letter: \"shutdown\": \"s\" (19). \"beebread\": \"b\" (2). \"conveyor\": \"c\" (3). \"courtyard\": \"c\" (3). \"semantic\": \"s\" (19). \"aqueduct\": \"a\" (1). \"lacewing\": \"l\" (12). \"grown\": \"g\" (7). \"mummy\": \"m\" (13). \"infinitude\": \"i\" (9). \"tennessee\": \"t\" (20). \"taillight\": \"t\" (20). \"monarch\": \"m\" (13). \"neural\": \"n\" (14). \"aristocrat\": \"a\" (1). \"topheavy\": \"t\" (20). \"flagler\": \"f\" (6). \"deviate\": \"d\" (4).
Thought 2: We now have: (1) [\"aristocrat\" ? \"aqueduct\"] < (2) \"beebread\" < (3) [\"conveyor\" ? \"courtyard\"] < (4) \"deviate\" < (6) \"flagler\" < (7) \"grown\" < (9) \"infinitude\" < (12) \"lacewing\" < (13) [\"mummy\" ? \"monarch\"] < (14) \"neural\" < (19) [\"semantic\" ? \"shutdown\"] < (20) [\"tennessee\" ? \"taillight\" ? \"topheavy\"].
Thought 3: Now let's sort this subpart [\"aristocrat\" ? \"aqueduct\"] by looking at their second letters. The second letter: \"aristocrat\": \"r\" (18). \"aqueduct\": \"q\" (17).
Thought 4: We now have: (17) \"aqueduct\" < (18) \"aristocrat\" for the subpart. Hence, we have \"aqueduct\" < \"aristocrat\" < \"beebread\" < [\"conveyor\" ? \"courtyard\"] < \"deviate\" < \"flagler\" < \"grown\" < \"infinitude\" < \"lacewing\" < [\"mummy\" ? \"monarch\"] < \"neural\" < [\"semantic\" ? \"shutdown\"] < [\"tennessee\" ? \"taillight\" ? \"topheavy\"].
Thought 5: Now let's sort this subpart [\"conveyor\" ? \"courtyard\"] by looking at their second letters. The second letter: \"conveyor\": \"o\" (15). \"courtyard\": \"o\" (15).
Thought 6: We now have: (15) [\"conveyor\" ? \"courtyard\"] for the subpart. Hence, we have \"aqueduct\" < \"aristocrat\" < \"beebread\" < [\"conveyor\" ? \"courtyard\"] < \"deviate\" < \"flagler\" < \"grown\" < \"infinitude\" < \"lacewing\" < [\"mummy\" ? \"monarch\"] < \"neural\" < [\"semantic\" ? \"shutdown\"] < [\"tennessee\" ? \"taillight\" ? \"topheavy\"].
Thought 7: Now let's sort this subpart [\"mummy\" ? \"monarch\"] by looking at their second letters. The second letter: \"mummy\": \"u\" (21). \"monarch\": \"o\" (15).
Thought 8: We now have: (15) \"monarch\" < (21) \"mummy\" for the subpart. Hence, we have \"aqueduct\" < \"aristocrat\" < \"beebread\" < [\"conveyor\" ? \"courtyard\"] < \"deviate\" < \"flagler\" < \"grown\" < \"infinitude\" < \"lacewing\" < \"monarch\" < \"mummy\" < \"neural\" < [\"semantic\" ? \"shutdown\"] < [\"tennessee\" ? \"taillight\" ? \"topheavy\"].
Thought 9: Now let's sort this subpart [\"semantic\" ? \"shutdown\"] by looking at their second letters. The second letter: \"semantic\": \"e\" (5). \"shutdown\": \"h\" (8).
Thought 10: We now have: (5) \"semantic\" < (8) \"shutdown\" for the subpart. Hence, we have \"aqueduct\" < \"aristocrat\" < \"beebread\" < [\"conveyor\" ? \"courtyard\"] < \"deviate\" < \"flagler\" < \"grown\" < \"infinitude\" < \"lacewing\" < \"monarch\" < \"mummy\" < \"neural\" < \"semantic\" < \"shutdown\" < [\"tennessee\" ? \"taillight\" ? \"topheavy\"].
Thought 11: Now let's sort this subpart [\"tennessee\" ? \"taillight\" ? \"topheavy\"] by looking at their second letters. The second letter: \"tennessee\": \"e\" (5). \"taillight\": \"a\" (1). \"topheavy\": \"o\" (15).
Thought 12: We now have: (1) \"taillight\" < (5) \"tennessee\" < (15) \"topheavy\" for the subpart. Hence, we have \"aqueduct\" < \"aristocrat\" < \"beebread\" < [\"conveyor\" ? \"courtyard\"] < \"deviate\" < \"flagler\" < \"grown\" < \"infinitude\" < \"lacewing\" < \"monarch\" < \"mummy\" < \"neural\" < \"semantic\" < \"shutdown\" < \"taillight\" < \"tennessee\" < \"topheavy\".
Thought 13: I have now sorted all the words. The answer is aqueduct aristocrat beebread conveyor courtyard deviate flagler grown infinitude lacewing mummy monarch neural semantic shutdown taillight tennessee topheavy
Q: Is there a mistake in this sequence? Write \"No\" if there are no mistakes, or the number N if there is a mistake in Thought N.

</example_2>
<example_3>

You are an expert in word sorting. You will be provided with a list of words and the steps taken, in the form of thoughts, to arrange them in alphabetical order.
Your job is to identify the first step that was a mistake in reasoning about the order of the words. This can be misunderstanding the order of
the alphabet or getting the word or letter wrong or missing a word entirely.
Q: Sort the following words alphabetically: List: balletomane brindisi mona secondhand blackstone effluvium beman swabby durward horse lament camille appetite mattock disputant
Thought 1: I should start by looking at the first letter of the words in the list. The first letter: \"balletomane\": \"b\" (2). \"brindisi\": \"b\" (2). \"mona\": \"m\" (13). \"secondhand\": \"s\" (19). \"blackstone\": \"b\" (2). \"effluvium\": \"e\" (5). \"beman\": \"b\" (2). \"swabby\": \"s\" (19). \"durward\": \"d\" (4). \"horse\": \"h\" (8). \"lament\": \"l\" (12). \"camille\": \"c\" (3). \"appetite\": \"a\" (1). \"mattock\": \"m\" (13). \"disputant\": \"d\" (4).
Thought 2: We now have: (1) \"appetite\" < (2) [\"balletomane\" ? \"brindisi\" ? \"blackstone\" ? \"beman\"] < (3) \"camille\" < (4) [\"durward\" ? \"disputant\"] < (5) \"effluvium\" < (8) \"horse\" < (12) \"lament\" < (13) [\"mona\" ? \"mattock\"] < (19) [\"secondhand\" ? \"swabby\"].
Thought 3: Now let's sort this subpart [\"balletomane\" ? \"brindisi\" ? \"blackstone\" ? \"beman\"] by looking at their second letters. The second letter: \"balletomane\": \"a\" (1). \"brindisi\": \"r\" (18). \"blackstone\": \"l\" (12). \"beman\": \"e\" (5).
Thought 4: We now have: (1) \"balletomane\" < (5) \"beman\" < (12) \"blackstone\" < (18) \"brindisi\" for the subpart. Hence, we have \"appetite\" < \"balletomane\" < \"beman\" < \"camille\" < [\"durward\" ? \"disputant\"] < \"effluvium\" < \"horse\" < \"lament\" < [\"mona\" ? \"mattock\"] < [\"secondhand\" ? \"swabby\"].
Thought 5: Now let's sort this subpart [\"durward\" ? \"disputant\"] by looking at their second letters. The second letter: \"durward\": \"u\" (21). \"disputant\": \"i\" (9).
Thought 6: We now have: (9) \"disputant\" < (21) \"durward\" for the subpart. Hence, we have \"appetite\" < \"balletomane\" < \"beman\" < \"camille\" < \"disputant\" < \"effluvium\" < \"horse\" < \"lament\" < [\"mona\" ? \"mattock\"] < [\"secondhand\" ? \"swabby\"] < \"durward\".
Thought 7: Now let's sort this subpart [\"mona\" ? \"mattock\"] by looking at their second letters. The second letter: \"mona\": \"o\" (15). \"mattock\": \"a\" (1).
Thought 8: We now have: (1) \"mattock\" < (15) \"mona\" for the subpart. Hence, we have \"appetite\" < \"balletomane\" < \"beman\" < \"camille\" < \"disputant\" < \"effluvium\" < \"horse\" < \"lament\" < \"mattock\" < [\"secondhand\" ? \"swabby\"] < \"durward\" < \"mona\".
Thought 9: Now let's sort this subpart [\"secondhand\" ? \"swabby\"] by looking at their second letters. The second letter: \"secondhand\": \"e\" (5). \"swabby\": \"w\" (23).
Thought 10: We now have: (5) \"secondhand\" < (23) \"swabby\" for the subpart. Hence, we have \"appetite\" < \"balletomane\" < \"beman\" < \"camille\" < \"disputant\" < \"effluvium\" < \"horse\" < \"lament\" < \"mattock\" < \"secondhand\" < \"swabby\" < \"durward\" < \"mona\".
Thought 11: I have now sorted all the words. The answer is appetite balletomane beman camille disputant effluvium horse lament mattock mona secondhand swabby durward
Q: Is there a mistake in this sequence? Write \"No\" if there are no mistakes, or the number N if there is a mistake in Thought N.

</example_3>
<example_4>

You are an expert in word sorting. You will be provided with a list of words and the steps taken, in the form of thoughts, to arrange them in alphabetical order.
Your job is to identify the first step that was a mistake in reasoning about the order of the words. This can be misunderstanding the order of
the alphabet or getting the word or letter wrong or missing a word entirely.
Q: Sort the following words alphabetically: List: fetal trilingual incredulous boulder ail ar deride right degas snowy verb origami penguin monsanto compute awash dyadic
Thought 1: I should start by looking at the first letter of the words in the list. The first letter: \"fetal\": \"f\" (6). \"trilingual\": \"t\" (20). \"incredulous\": \"i\" (9). \"boulder\": \"b\" (2). \"ail\": \"a\" (1). \"ar\": \"a\" (1). \"deride\": \"d\" (4). \"right\": \"r\" (18). \"degas\": \"d\" (4). \"snowy\": \"s\" (19). \"verb\": \"v\" (22). \"origami\": \"o\" (15). \"penguin\": \"p\" (16). \"monsanto\": \"m\" (13). \"compute\": \"c\" (3). \"awash\": \"a\" (1). \"dyadic\": \"d\" (4).
Thought 2: We now have: (1) [\"ail\" ? \"ar\" ? \"awash\"] < (2) \"boulder\" < (3) \"compute\" < (4) [\"deride\" ? \"degas\" ? \"dyadic\"] < (6) \"fetal\" < (9) \"incredulous\" < (13) \"monsanto\" < (15) \"origami\" < (16) \"penguin\" < (18) \"right\" < (19) \"snowy\" < (20) \"trilingual\" < (22) \"verb\".
Thought 3: Now let's sort this subpart [\"ail\" ? \"ar\" ? \"awash\"] by looking at their second letters. The second letter: \"ail\": \"i\" (9). \"ar\": \"r\" (18). \"awash\": \"w\" (23).
Thought 4: We now have: (9) \"ail\" < (18) \"ar\" < (23) \"awash\" for the subpart. Hence, we have [\"ail\" ? \"ar\" ? \"awash\"] < (2) \"boulder\" < (3) \"compute\" < (4) [\"deride\" ? \"degas\" ? \"dyadic\"] < (6) \"fetal\" < (9) \"incredulous\" < (13) \"monsanto\" < (15) \"origami\" < (16) \"penguin\" < (18) \"right\" < (19) \"snowy\" < (20) \"trilingual\" < (22) \"verb\".
Thought 5: Now let's sort this subpart [\"deride\" ? \"degas\" ? \"dyadic\"] by looking at their second letters. The second letter: \"deride\": \"e\" (5). \"degas\": \"e\" (5). \"dyadic\": \"y\" (25).
Thought 6: We now have: (5) [\"deride\" ? \"degas\"] < (25) \"dyadic\" for the subpart. Hence, we have [\"ail\" ? \"ar\" ? \"awash\"] < (2) \"boulder\" < (3) \"compute\" < (4) [\"deride\" ? \"degas\"] < (5) \"dyadic\" < (6) \"fetal\" < (9) \"incredulous\" < (13) \"monsanto\" < (15) \"origami\" < (16) \"penguin\" < (18) \"right\" < (19) \"snowy\" < (20) \"trilingual\" < (22) \"verb\".
Thought 7: Now let's sort this subpart [\"ail\" ? \"ar\" ? \"awash\"] by looking at their third letters. The third letter: \"ail\": \"l\" (12). \"ar\": \"r\" (18). \"awash\": \"s\" (19).
Thought 8: We now have: (12) \"ail\" < (18) \"ar\" < (19) \"awash\" for the subpart. Hence, we have \"ail\" < \"ar\" < \"awash\" < (2) \"boulder\" < (3) \"compute\" < (4) [\"deride\" ? \"degas\"] < (5) \"dyadic\" < (6) \"fetal\" < (9) \"incredulous\" < (13) \"monsanto\" < (15) \"origami\" < (16) \"penguin\" < (18) \"right\" < (19) \"snowy\" < (20) \"trilingual\" < (22) \"verb\".
Thought 9: Now let's sort this subpart [\"deride\" ? \"degas\"] by looking at their third letters. The third letter: \"deride\": \"r\" (18). \"degas\": \"s\" (19).
Thought 10: We now have: (18) \"deride\" < (19) \"degas\" for the subpart. Hence, we have \"ail\" < \"ar\" < \"awash\" < (2) \"boulder\" < (3) \"compute\" < (4) \"deride\" < (5) \"dyadic\" < (6) \"fetal\" < (9) \"incredulous\" < (13) \"monsanto\" < (15) \"origami\" < (16) \"penguin\" < (18) \"right\" < (19) \"snowy\" < (20) \"trilingual\" < (22) \"verb\".
Thought 11: I have now sorted all the words. The answer is ail ar awash boulder compute deride degas dyadic fetal incredulous monsanto origami penguin right snowy trilingual verb
Q: Is there a mistake in this sequence? Write \"No\" if there are no mistakes, or the number N if there is a mistake in Thought N.

</example_4>
<example_5>

You are an expert in word sorting. You will be provided with a list of words and the steps taken, in the form of thoughts, to arrange them in alphabetical order.
Your job is to identify the first step that was a mistake in reasoning about the order of the words. This can be misunderstanding the order of
the alphabet or getting the word or letter wrong or missing a word entirely.
Q: Sort the following words alphabetically: List: yves butt scribe seaworthy manumitted clapeyron lift blackguard reconnaissance agile woodcut lightfooted sawbelly meager geophysical wiseacre mathieu cognoscenti purposive flamboyant
Thought 1: I should start by looking at the first letter of the words in the list. The first letter: \"yves\": \"y\" (25). \"butt\": \"b\" (2). \"scribe\": \"s\" (19). \"seaworthy\": \"s\" (19). \"manumitted\": \"m\" (13). \"clapeyron\": \"c\" (3). \"lift\": \"l\" (12). \"blackguard\": \"b\" (2). \"reconnaissance\": \"r\" (18). \"agile\": \"a\" (1). \"woodcut\": \"w\" (23). \"lightfooted\": \"l\" (12). \"sawbelly\": \"s\" (19). \"meager\": \"m\" (13). \"geophysical\": \"g\" (7). \"wiseacre\": \"w\" (23). \"mathieu\": \"m\" (13). \"cognoscenti\": \"c\" (3). \"purposive\": \"p\" (16). \"flamboyant\": \"f\" (6).
Thought 2: We now have: (1) \"agile\" < (2) [\"butt\" ? \"blackguard\"] < (3) [\"clapeyron\" ? \"cognoscenti\"] < (6) \"flamboyant\" < (7) \"geophysical\" < (12) [\"lift\" ? \"lightfooted\"] < (13) [\"manumitted\" ? \"mathieu\"] < (16) \"purposive\" < (18) \"reconnaissance\" < (19) [\"scribe\" ? \"seaworthy\" ? \"sawbelly\"] < (23) [\"woodcut\" ? \"wiseacre\"] < (25) \"yves\".
Thought 3: Now let's sort this subpart [\"butt\" ? \"blackguard\"] by looking at their second letters. The second letter: \"butt\": \"u\" (21). \"blackguard\": \"l\" (12).
Thought 4: We now have: (12) \"blackguard\" < (21) \"butt\" for the subpart. Hence, we have \"agile\" < \"blackguard\" < \"butt\" < [\"clapeyron\" ? \"cognoscenti\"] < \"flamboyant\" < \"geophysical\" < [\"lift\" ? \"lightfooted\"] < [\"manumitted\" ? \"mathieu\"] < \"purposive\" < \"reconnaissance\" < [\"scribe\" ? \"seaworthy\" ? \"sawbelly\"] < [\"woodcut\" ? \"wiseacre\"] < \"yves\".
Thought 5: Now let's sort this subpart [\"clapeyron\" ? \"cognoscenti\"] by looking at their second letters. The second letter: \"clapeyron\": \"l\" (12). \"cognoscenti\": \"o\" (15).
Thought 6: We now have: (12) \"clapeyron\" < (15) \"cognoscenti\" for the subpart. Hence, we have \"agile\" < \"blackguard\" < \"butt\" < \"clapeyron\" < \"cognoscenti\" < \"flamboyant\" < \"geophysical\" < [\"lift\" ? \"lightfooted\"] < [\"manumitted\" ? \"mathieu\"] < \"purposive\" < \"reconnaissance\" < [\"scribe\" ? \"seaworthy\" ? \"sawbelly\"] < [\"woodcut\" ? \"wiseacre\"] < \"yves\".
Thought 7: Now let's sort this subpart [\"lift\" ? \"lightfooted\"] by looking at their second letters. The second letter: \"lift\": \"i\" (9). \"lightfooted\": \"i\" (9).
Thought 8: We now have: (9) [\"lift\" ? \"lightfooted\"] for the subpart. Hence, we have \"agile\" < \"blackguard\" < \"butt\" < \"clapeyron\" < \"cognoscenti\" < \"flamboyant\" < \"geophysical\" < [\"lift\" ? \"lightfooted\"] < [\"manumitted\" ? \"mathieu\"] < \"purposive\" < \"reconnaissance\" < [\"scribe\" ? \"seaworthy\" ? \"sawbelly\"] < [\"woodcut\" ? \"wiseacre\"] < \"yves\".
Thought 9: Now let's sort this subpart [\"manumitted\" ? \"mathieu\"] by looking at their second letters. The second letter: \"manumitted\": \"a\" (1). \"mathieu\": \"a\" (1).
Thought 10: We now have: (1) [\"manumitted\" ? \"mathieu\"] for the subpart. Hence, we have \"agile\" < \"blackguard\" < \"butt\" < \"clapeyron\" < \"cognoscenti\" < \"flamboyant\" < \"geophysical\" < [\"lift\" ? \"lightfooted\"] < [\"manumitted\" ? \"mathieu\"] < \"purposive\" < \"reconnaissance\" < [\"scribe\" ? \"seaworthy\" ? \"sawbelly\"] < [\"woodcut\" ? \"wiseacre\"] < \"yves\".
Thought 11: Now let's sort this subpart [\"scribe\" ? \"seaworthy\" ? \"sawbelly\"] by looking at their second letters. The second letter: \"scribe\": \"c\" (3). \"seaworthy\": \"e\" (5). \"sawbelly\": \"a\" (1).
Thought 12: We now have: (1) \"sawbelly\" < (3) \"scribe\" < (5) \"seaworthy\" for the subpart. Hence, we have \"agile\" < \"blackguard\" < \"butt\" < \"clapeyron\" < \"cognoscenti\" < \"flamboyant\" < \"geophysical\" < [\"lift\" ? \"lightfooted\"] < [\"manumitted\" ? \"mathieu\"] < \"purposive\" < \"reconnaissance\" < \"sawbelly\" < \"scribe\" < \"seaworthy\" < [\"woodcut\" ? \"wiseacre\"] < \"yves\".
Thought 13: Now let's sort this subpart [\"woodcut\" ? \"wiseacre\"] by looking at their second letters. The second letter: \"woodcut\": \"o\" (15). \"wiseacre\": \"i\" (9).
Thought 14: We now have: (9) \"wiseacre\" < (15) \"woodcut\" for the subpart. Hence, we have \"agile\" < \"blackguard\" < \"butt\" < \"clapeyron\" < \"cognoscenti\" < \"flamboyant\" < \"geophysical\" < [\"lift\" ? \"lightfooted\"] < [\"manumitted\" ? \"mathieu\"] < \"purposive\" < \"reconnaissance\" < \"sawbelly\" < \"scribe\" < \"seaworthy\" < \"wiseacre\" < \"woodcut\" < \"yves\".
Thought 15: Now let's sort this subpart [\"lift\" ? \"lightfooted\"] by looking at their third letters. The third letter: \"lift\": \"f\" (6). \"lightfooted\": \"t\" (20).
Thought 16: We now have: (6) \"lift\" < (20) \"lightfooted\" for the subpart. Hence, we have \"agile\" < \"blackguard\" < \"butt\" < \"clapeyron\" < \"cognoscenti\" < \"flamboyant\" < \"geophysical\" < \"lift\" < \"lightfooted\" < [\"manumitted\" ? \"mathieu\"] < \"purposive\" < \"reconnaissance\" < \"sawbelly\" < \"scribe\" < \"seaworthy\" < \"wiseacre\" < \"woodcut\" < \"yves\".
Thought 17: Now let's sort this subpart [\"manumitted\" ? \"mathieu\"] by looking at their third letters. The third letter: \"manumitted\": \"n\" (14). \"mathieu\": \"t\" (20).
Thought 18: We now have: (14) \"manumitted\" < (20) \"mathieu\" for the subpart. Hence, we have \"agile\" < \"blackguard\" < \"butt\" < \"clapeyron\" < \"cognoscenti\" < \"flamboyant\" < \"geophysical\" < \"lift\" < \"lightfooted\" < \"manumitted\" < \"mathieu\" < \"purposive\" < \"reconnaissance\" < \"sawbelly\" < \"scribe\" < \"seaworthy\" < \"wiseacre\" < \"woodcut\" < \"yves\".
Thought 19: I have now sorted all the words. The answer is agile blackguard butt clapeyron cognoscenti flamboyant geophysical lift lightfooted manumitted mathieu meager purposive reconnaissance sawbelly scribe seaworthy woodcut wiseacre yves
Q: Is there a mistake in this sequence? Write \"No\" if there are no mistakes, or the number N if there is a mistake in Thought N.

</example_5>


请完成上述谜题的训练场环境类实现，包括所有必要的方法。
"""

from internbootcamp.bootcamp.base import Basebootcamp
import re
import random
import json
import string
# from nltk.corpus import words as whole_words


class BbehWordSortingbootcamp(Basebootcamp):
    SUPPORTED_SUBTASKS = ["error_detection", "pure_sort"]
    SORT_ORDER = ["normal_order", "custom_sorting"]
    MODES = ["normal", "reverse"]

    def __init__(self, **params):
        super().__init__(**params)
        self.max_word_list_size = params.get("max_word_list_size", 16)
        self.min_word_list_size = params.get("min_word_list_size", 8)
        self.subtask_ratio = params.get("subtask_ratio", 0.5)  # 子任务1占比
        self.mode_ratio = params.get("mode_ratio", 0.5)
        self.order_ratio = params.get("order_ratio", 0.5)
        # self.alphabet = self._generate_alphabet(params.get('letter_swaps', self.LETTER_SWAPS))
        internbootcamp_path = "/".join(__file__.split('/')[:-3])
        with open(f'{internbootcamp_path}/libs/data/words_alpha_370000.txt', 'r') as f:
            words = f.readlines()
            words = [w.strip() for w in words]
        self.word_pool = words
        

    def case_generator(self):
        """生成包含两种子任务的案例"""
        subtask = random.choices(
            self.SUPPORTED_SUBTASKS,
            weights=[self.subtask_ratio, 1 - self.subtask_ratio],
            k=1,
        )[0]
        enable_error = True if subtask == "error_detection" else False
        mode = random.choices(
            self.MODES, weights=[self.mode_ratio, 1 - self.mode_ratio], k=1
        )[0]
        sort_order = random.choice(self.SORT_ORDER)

        custom_order = None
        if sort_order == "custom_sorting":
            letters = list(string.ascii_lowercase)
            random.shuffle(letters)
            custom_order = letters

        word_list_size = random.randint(
            self.min_word_list_size, self.max_word_list_size
        )
        words = random.sample(self.word_pool, word_list_size)
        words = [w.lower() for w in words]

        meta_info = self._verbal_sort_words(
            word_list=words,
            mode=mode,
            custom_order=custom_order,
            enable_error=enable_error,
        )
        if subtask == "error_detection":
            while len(meta_info["thoughts"]) < word_list_size:
                words = random.sample(self.word_pool, word_list_size)
                words = [w.lower() for w in words]
                meta_info = self._verbal_sort_words(
                    word_list=words,
                    mode=mode,
                    custom_order=custom_order,
                    enable_error=enable_error,
                )

        meta_info["words"] = words
        meta_info["subtask"] = subtask
        meta_info["mode"] = mode
        meta_info["sort_order"] = sort_order
        meta_info["custom_order"] = custom_order
        return meta_info

    @staticmethod
    def prompt_func(case) -> str:
        
        prompt = ""
        special_requirements = ""

        if case["custom_order"] is not None:
            special_requirements += f"""
You need to sort the words according to a custom alphabet. The custom order is: {', '.join(case['custom_order'])}
"""

        if case["mode"] == "reverse":
            special_requirements += f"""
Add a new sorting rule. When sorting the words, you need to sort the letters in reverse order, comparing from right to left instead of left to right.
"""
        if special_requirements != "":
            special_requirements = "There are some special requirements:\n" + special_requirements
        if case["subtask"] == "error_detection":
            prompt = """
You are an expert in word sorting. You will be provided with a list of words and the steps taken, in the form of thoughts.
Your job is to identify the first step that was a mistake in reasoning about the order of the words. This can be misunderstanding the order of
the alphabet or getting the word or letter wrong or missing a word entirely.
"""
            prompt += f"""Q: Sort the following words: List: {" ".join(case['words'])}
{special_requirements}
{chr(10).join(f"Thought {i+1}: {t}" for i, t in enumerate(case['thoughts']))}

Q: Is there a mistake in this sequence? Write \"No\" if there are no mistakes, or the number N if there is a mistake in Thought N.
Please reason step by step and put your final answer within [answer] [/answer] tags.
"""
        else:
            prompt = f"""Sort the following words with the new alphabet and separate them with comma: {", ".join(case['words'])}
{special_requirements}
Format your final answer as: [answer]<comma-separated words>[/answer].
Please reason step by step and put your final answer within [answer] [/answer] tags."""

        return prompt

    @staticmethod
    def extract_output(output):
        """提取两种子任务的答案"""
        answer_match = re.search(r"\[answer\](.*?)\[/answer\]", output, re.DOTALL)
        if not answer_match:
            return None

        answer = answer_match.group(1).strip()

        # 尝试解析为错误步骤编号
        if answer.lower() == "no":
            return "No"
        try:
            return int(answer)
        except ValueError:
            # 可能是子任务2的列表答案
            try:
                return json.loads(answer)
            except:
                return [w.strip() for w in answer.split(",")]

    @classmethod
    def _verify_correction(cls, solution, case):
        """根据子任务类型验证答案"""
        if case["subtask"] == "error_detection":
            expected = case["first_error_step"]
            return str(solution) == str(expected)
        else:
            # 验证排序结果与自定义字母表一致
            try:
                expected = case["sorted_words"]
                return solution == expected
            except:
                return False

    def _verbal_sort_words(
        self, word_list, mode="normal", custom_order=None, enable_error=True
    ):
        if custom_order is not None:
            key_map = {char: i for i, char in enumerate(custom_order)}
            key_map[""] = -1
        assert mode in ["normal", "reverse"], "Sort mode should in [normal, reverse]!"

        def get_key(word, depth):
            if mode == "normal":  # 正序
                return word[depth] if len(word) > depth else ""
            elif mode == "reverse":  # 反序
                return word[-(depth + 1)] if len(word) > depth else ""

        def verbal_sort_step(words, depth=0):
            if len(words) <= 1:
                return words

            # 1. 提取当前字符进行分组
            grouped = {}
            reverve_group = {}
            for word in words:
                # generate error
                # missing the letter
                if enable_error and random.random() < 0.02:
                    if verbal_sort_step.first_error_step is None:
                        verbal_sort_step.first_error_step = verbal_sort_step.thought_count
                    continue
                key = get_key(word, depth)
                if enable_error and random.random() < 0.02:
                    error_key = random.choice(word)
                    if error_key != key:
                        key = error_key
                        if verbal_sort_step.first_error_step is None:
                            verbal_sort_step.first_error_step = verbal_sort_step.thought_count
                grouped.setdefault(key, []).append(word)
                reverve_group[word] = key
            # 2. 输出当前分组情况
            try:
                sorted_keys = sorted(
                    grouped.keys(),
                    key=lambda k: key_map[k] if custom_order and k in key_map else k,
                )
            except Exception as e:
                # 
                pass
                
            
            verbal_letters = ""
            verbal_letters += f"The {number_to_ordinal(depth + 1)} letter: "
            for word in reverve_group.keys():
                verbal_letters += f"{word}: {reverve_group[word]}. "
            correct_sorted_keyes = sorted_keys.copy()

            special_prompt = "" if mode == "normal" else " from right to left"
            if verbal_sort_step.thought_count == 1:
                thought = f"I should start by looking at the first letter of the words in the list. "
            else:
                thought = f"Now let's sort this subpart {words}. Looking at the {number_to_ordinal(depth + 1)} letters{special_prompt}."
            thought += verbal_letters
            verbal_sort_step.thought_list.append(thought)
            verbal_sort_step.thought_count += 1

            # 3. 更新全局状态并输出
            new_global_state = []
            global_state = verbal_sort_step.global_state.copy()
            for group in global_state:
                if set(group) == set(words):
                    for key in sorted_keys:
                        new_global_state.append(grouped[key])
                else:
                    new_global_state.append(group)

            # 随机生成错误
            if enable_error and random.random() < 0.2:  # 20% 的概率生成错误
                # 错误类型1: 错误的比较逻辑
                rnd = random.random()
                if rnd < 0.3:
                    sorted_keys = sorted(
                        grouped.keys(),
                        reverse=True,
                        key=lambda k: (
                            key_map[k] if custom_order and k in key_map else k
                        ),
                    )  # 错误地反向排序
                elif rnd < 0.7:
                    random.shuffle(sorted_keys)
                else:
                    sorted_keys = list(grouped.keys())  # 错误地不排序
                if (
                    verbal_sort_step.first_error_step is None
                    and sorted_keys != correct_sorted_keyes
                ):
                    verbal_sort_step.first_error_step = verbal_sort_step.thought_count

            # 随机生成错误
            if enable_error and random.random() < 0.2:  # 20% 的概率生成错误
                # 错误类型2: 错误的全局状态更新
                # 随机打乱global state
                global_state = new_global_state
                random.shuffle(global_state)
                if verbal_sort_step.first_error_step is None:
                    verbal_sort_step.first_error_step = verbal_sort_step.thought_count
            else:
                global_state = new_global_state
            verbal_sort_step.global_state = global_state
            
            thought = f"We now have: "
            thought += " < ".join(
                [
                    f"{grouped[k] if len(grouped[k]) > 1 else grouped[k][0]}"
                    for k in sorted_keys
                ]
            )
            if verbal_sort_step.thought_count != 2:
                thought += "for the subpart. Hence, we have "
                thought += " < ".join(
                    [f"{group if len(group) > 1 else group[0]}" for group in global_state]
                )
            
            verbal_sort_step.thought_list.append(thought)
            verbal_sort_step.thought_count += 1

            # 4. 递归对子序列排序
            sorted_words = []
            for key in sorted_keys:
                new_words = verbal_sort_step(grouped[key], depth + 1)
                sorted_words.extend(new_words)

            return sorted_words

        verbal_sort_step.thought_count = 1
        verbal_sort_step.thought_list = []
        verbal_sort_step.first_error_step = None
        verbal_sort_step.global_state = [word_list.copy()]
        sorted_words = verbal_sort_step(word_list)
        answer_thought = "I have now sorted all the words. The answer is " + " ".join(sorted_words)
        verbal_sort_step.thought_list.append(answer_thought)
        return {
            "thoughts": verbal_sort_step.thought_list,
            "first_error_step": (
                "No"
                if verbal_sort_step.first_error_step is None
                else verbal_sort_step.first_error_step
            ),
            "sorted_words": sorted_words,
        }


def number_to_ordinal(n):
    ordinals = {
        1: "first",
        2: "second",
        3: "third",
        4: "fourth",
        5: "fifth",
        6: "sixth",
        7: "seventh",
        8: "eighth",
        9: "ninth",
        10: "tenth"
    }
    
    return ordinals.get(n, f"{n}th")

if __name__ == "__main__":
    bootcamp = BbehWordSortingbootcamp()
    case = bootcamp.case_generator()
    print(case)
    prompt = bootcamp.prompt_func(case)
    print(f"prompt: {prompt}")

    if case["subtask"] == "error_detection":
        answer = case["first_error_step"]
    else:
        answer = ", ".join(case["sorted_words"])
    answer = f"[answer]{answer}[/answer]"
    print(f"answer: {answer}")

    extracted_output = bootcamp.extract_output(answer)
    print(f"extracted_output: {extracted_output}")

    verify_result = bootcamp.verify_score(answer, case)
    print(f"verify_result: {verify_result}")
